Year: 2026
Type: preprint
Abstract: We establish Bourgain--Brezis selection maps for Hodge systems in new ranges of Besov and Triebel--Lizorkin spaces. Our approach combines the trace-free Beurling--Ahlfors transform with a nonlinear duality method. To control concentrations, we use tools developed by Stolyarov in the study of Maz'ya's $Φ$-inequalities. These methods yield selection maps in Besov spaces $\dot B^{n/p}_{p,q}(\mathbb{R}^n)$ for every $1\leq q\leq p\leq 2$, and in Triebel--Lizorkin spaces $\dot F^{n/p}_{p,q}(\mathbb{R}^n)$ for every $1
Source: arXiv (Cornell University)
Author: Arsénio, Diogo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214721165